many of us using blogger blogspot blog for blogging, because it is easy to use and editable.
but after a while you want to your blog look more professional and more credible by Publish on a custom domain .
because some people think that yourblogname.blogspot.com used by newbies only, That’s not always true, of course.
there is 2 ways to do it,
1- Point your already owned and registered domain name to your blog.
2- buy new domain name via your blogger account.
we’ll now talk about number 2.
buy new domain name via your blogger account.
now blogger makes it easier to convert your Blogspot Account Into A .com Domain
when you register a domain name via blogger account your Domain will be registered through a Google partner and cost $10 (USD) for one year.and as part of registration, you will also get a Google Apps account for your new domain.
and the great deal here is that YourBlogName.blogspot.com will redirect to your new custom domain. so you won’t leave your readers behind!
the first thing to to is to log into your blogger account,
Then got to Settings >> Publishing
FIND : Switch to: • Custom Domain
and click Custom Domain
for more detail check next image

FIND : What address would you like your blog to have? next to this you’ll find a small text filed, fill it by your custom domain name, and click Check Availability

if the name you entered is Available you will navigate to Choose a domain name (step 1 of 3) page
click continue to registration
after that you’ll navigate to Sign up (step 2 of 3) page.
Enter the domain registration information for your chosen domain name.
and note that this information will be listed in whois directory.
then click i accept, process to Google checkout.
if you already have credit card added to your Google account, you can easily press agree and continue
Or you have to add your billing information, credit card number and details to your current Google account.
once you are finished press agree and continue.
next review your purchase and press place your order now.
now your custom domain is setup.
you are finish, please note that it may take 2 for 3 days to your blog to transformation to your new domain.
finally here is video helps you to do it in the right way.

And of curse you can use any domain owned for you from another web company, But in choosing custom domains, be sure to secure your sites with the best web hosting solutions.